Finite Group Databasebeta

← #20255917

Subgroups — #20255917

Order 6016.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689847C211yesmaximal, characteristic
2#15689811C211yesmaximal, characteristic
3#15689467C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689466C211yesmaximal, characteristic, complemented
6#15689460C211yesmaximal, characteristic, complemented
7#15689427C211yesmaximal, characteristic, complemented
8#15689415C211yesmaximal, characteristic, complemented
9#15689382C211yesmaximal, characteristic, complemented
10#15689365C211yesmaximal, characteristic, complemented
11#15689231C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic
13#15689164C211yesmaximal, characteristic, complemented
14#15689158C211yesmaximal, characteristic, complemented
15C47×#501C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094019—21no—
20#13094019—21no—
21#13094019—21no—
22#13094015—21no—
23#13094013—21no—
24#13094009—21no—
25#13094004C2211yescharacteristic
26#13094004C2211yescharacteristic
27#13094004C2211yescharacteristic
28#13094004C2211yescharacteristic
29Q8×Dic47—21no—
30C4×Dic94C2211yescharacteristic
31C4×Dic94C2211yescharacteristic
32C4×D188C2211yescharacteristic
33#13093982—21no—
34#13093982C2211yescharacteristic
35#13093982C2211yescharacteristic
36#13093982C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093947C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D188D411yescharacteristic
61C2×C4×D47—21no—
62C2×C4×D47C2311yescharacteristic
63C2×C4×D47C2311yescharacteristic
64C2×Dic94C2311yescharacteristic
65C2×Dic94C2311yescharacteristic
66C2×C8×C47C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C42×C47C2311yescharacteristic
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4D411yescharacteristic
84(C2×D47)⋊C4D411yescharacteristic
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47D411yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95C4×Dic47—21no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102Dic188—22no—
103#10625324—22no—
104C8×D47—22no—
105C22×D47C2×D411yescharacteristic
106C22×D47C2×D411yescharacteristic
107Q8×C47—42no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121D188—41no—
122C4×D47—21no—
123C4×D47—21no—
124C4×D47—21no—
125C4×D47—21no—
126C4×D47—42no—
127Dic94—21no—
128Dic94—21no—
129Dic94—21no—
130Dic94—21no—
131C8×C47—21no—
132C8×C47#4112yes—
133C47⋊C8—21no—
134C47⋊C8—21no—
135C22×C47C22×D411yescharacteristic
136C2×D47—21no—
137C2×D47—21no—
138C2×D47—21no—
139C2×D47—21no—
140C2×D47—21no—
141C2×D47—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47C2×#4111yescharacteristic
149C4×C472−1+411yescharacteristic
150Dic47—21no—
151Dic47—21no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156#3349—471nomaximal, Sylow
157C2×C47#54711yescharacteristic
158C2×C47#57511yescharacteristic
159C2×C47#57811yescharacteristic
160D47—41no—
161D47—41no—
162#556—471no—
163#552—471no—
164#501D4711yescharacteristic, complemented
165#485—471no—
166#485—471no—
167#485—471no—
168#484—471no—
169#479—471no—
170#477—471no—
171#470—471no—
172#467—471no—
173#441—471no—
174#435—471no—
175#428—471no—
176#427—471no—
177C47#334911yescharacteristic, complemented, Sylow
178C2×Q16—471no—
179C2×M16—471no—
180C22×C8—471no—
181C4⋊Q8C2×D4711yescharacteristic
182#126—941no—
183#126—941no—
184#126—941no—
185#125—941no—
186#125C2×D4711yescharacteristic
187#124—941no—
188#123—941no—
189C22⋊Q8—471no—
190C22⋊Q8—471no—
191C22⋊Q8—471no—
192C22⋊Q8—471no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×Q8—941no—
196C4×D4—471no—
197#117—471no—
198#117—471no—
199#117—471no—
200#117—941no—
201C2×C4⋊C4—471no—
202#107—471no—
203#107—471no—
204#107—471no—
205#107C2×D4711yescharacteristic
206#107C2×D4711yescharacteristic
207#106—471no—
208#106—471no—
209#106C2×D4711yescharacteristic
210#106C2×D4711yescharacteristic
211C4⋊C8—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218C22⋊C8—471no—
219C22⋊C8—471no—
220#97C2×D4711yescharacteristic
221C2×Q8—21no—
222C2×Q8—471no—
223C2×Q8—471no—
224C2×D4—471no—
225C22×C4—471no—
226C22×C4—471no—
227C22×C4—941no—
228Q16—942no—
229M16—942no—
230C2×C8—471no—
231C2×C8—471no—
232C2×C8—942no—
233C2×C8C22×D4711yescharacteristic
234C2×C8C22×D4711yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4C22×D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C4⋊C4C22×D4711yescharacteristic
251C4⋊C4C22×D4711yescharacteristic
252C22⋊C4—471no—
253C22⋊C4—471no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4—941no—
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C42—941no—
262C42—941no—
263C42—941no—
264C42—941no—
265C42—941no—
266C42C22×D4711yescharacteristic
267C23—471no—
268C23—471no—
269Q8—42no—
270Q8—941no—
271Q8—941no—
272Q8—941no—
273Q8—941no—
274D4—1881no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—471no—
280C2×C4—471no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—1882no—
290C2×C4D4×D4711yescharacteristic
291C2×C4D4×D4711yescharacteristic
292C2×C4C23×D4711yescharacteristic
293C8—21no—
294C8—941no—
295C8—941no—
296C8#1062535412yes—
297C22—941no—
298C22—941no—
299C22—941no—
300C22—941no—
301C22—941no—
302C22—941no—
303C22C2×D4×D4711yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—941no—
311C4—941no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4—1881no—
316C4C2×#1062535411yescharacteristic
317C4#1309407211yescharacteristic
318C2—1881no—
319C2—1881no—
320C2#1568977611yescharacteristic
321C2#1568991911yescharacteristic
322C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3349
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #15689467C2semidirect
4. #15689467C2semidirect
5. #15689466C2semidirect
6. #15689460C2semidirect
7. #15689427C2semidirect
8. #15689415C2semidirect
9. #15689382C2semidirect
10. #15689365C2semidirect
11. #15689231C2semidirect
13. #15689164C2semidirect
14. #15689158C2semidirect
15. C47×#501C2semidirect
164. #501D47semidirect
177. C47#3349semidirect